Sagnac effect in a chain of mesoscopic quantum rings

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10^{10} enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one dimensional chain of N coherently coupled quantum rings in the presence of a rotation of angular frequency, \Omega. We show that the transmission probability, T, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing N, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of \Omega with a slope \partialT/\partial \Omega N^2. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder and leads to a phase sensitivity well below the standard quantum limit

Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.Comment: revtex, 15 pages,8 figure

Phase Conjugation of a Quantum-Degenerate Atomic Fermi Beam

We discuss the possibility of phase-conjugation of an atomic Fermi field via nonlinear wave mixing in an ultracold gas. It is shown that for a beam of fermions incident on an atomic phase-conjugate mirror, a time reversed backward propagating fermionic beam is generated similar to the case in nonlinear optics. By adopting an operational definition of the phase, we show that it is possible to infer the presence of the phase-conjugate field by the loss of the interference pattern in an atomic interferometer

Spin current and shot noise from a quantum dot coupled to a quantized cavity field

We examine the spin current and the associated shot noise generated in a quantum dot connected to normal leads with zero bias voltage across the dot. The spin current is generated by spin flip transitions induced by a quantized electromagnetic field inside a cavity with one of the Zeeman states lying below the Fermi level of the leads and the other above. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics. We also calculate the photon current and photon current shot noise resulting from photons leaking out of the cavity. We show that the photon current is equal to the spin current and that the spin current can be significantly larger than for the case of a classical driving field as a result of cavity losses. In addition to this, the frequency dependent spin (photon) current shot noise show dips (peaks) that are a result of the discrete nature of photons

Measuring dark energy spatial inhomogeneity with supernova data

The gravitational lensing distortion of distant sources by the large-scale distribution of matter in the Universe has been extensively studied. In contrast, very little is known about the effects due to the large-scale distribution of dark energy. We discuss the use of Type Ia supernovae as probes of the spatial inhomogeneity and anisotropy of dark energy. We show that a shallow, almost all-sky survey can limit rms dark energy fluctuations at the horizon scale down to a fractional energy density of ~10^-4Comment: 4 pages; PRL submitte

A two measure model of dark energy and dark matter

In this work we construct a unified model of dark energy and dark matter. This is done with the following three elements: a gravitating scalar field, phi with a non-conventional kinetic term, as in the string theory tachyon; an arbitrary potential, V(phi); two measures -- a metric measure (sqrt{-g}) and a non-metric measure (Phi). The model has two interesting features: (i) For potentials which are unstable and would give rise to tachyonic scalar field, this model can stabilize the scalar field. (ii) The form of the dark energy and dark matter that results from this model is fairly insensitive to the exact form of the scalar field potential.Comment: 8 pages,no figures, revtex, typos corrected to match published versio

Boson-Fermion coherence in a spherically symmetric harmonic trap

We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudo-spin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.Comment: 16 pages, 14 figure

Quantum bistability and spin current shot noise of a single quantum dot coupled to an optical microcavity

Here we explore spin dependent quantum transport through a single quantum dot coupled to an optical microcavity. The spin current is generated by electron tunneling between a single doped reservoir and the dot combined with intradot spin flip transitions induced by a quantized cavity mode. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics and generates a pure spin current in the absence of any charge current. Earlier research has shown that in the classical limit where a large number of such dots interact with the cavity field, the spin current exhibits bistability as a function of the laser amplitude that drives the cavity. We show that in the limit of a single quantum dot this bistability continues to be present in the intracavity photon statistics. Signatures of the bistable photon statistics manifest themselves in the frequency dependent shot noise of the spin current despite the fact that the quantum mechanical average spin current no longer exhibits bistability. Besides having significance for future quantum dot based optoelectronic devices, our results shed light on the relation between bistability, which is traditionally viewed as a classical effect, and quantum mechanics

Cosmological Evolution of a Tachyon-Quintom Model of Dark Energy

In this work we study the cosmological evolution of a dark energy model with two scalar fields, i.e. the tachyon and the phantom tachyon. This model enables the equation of state $w$ to change from $w>-1$ to $w<-1$ in the evolution of the universe. The phase-space analysis for such a system with inverse square potentials shows that there exists a unique stable critical point, which has power-law solutions. In this paper, we also study another form of tachyon-quintom model with two fields, which voluntarily involves the interactions between both fields.Comment: 17 pages, 10 figure

Discriminating Electroweak-ino Parameter Ordering at the LHC and Its Impact on LFV Studies

Current limit on the dark matter relic abundance may suggest that $|\mu|$ should be smaller than prediction in the minimal supergravity scenario (mSUGRA) for moderate $m_0$ and $m_{1/2}$. The electroweak-ino parameter $M_1, M_2$ and $|\mu|$ are then much closer to each other. This can be realized naturally in the non-universal Higgs mass model (NUHM). Since the heaviest neutralino ($\tilde\chi^0_4$) and chargino ($\tilde\chi^\pm_2$) have significant gaugino components, they may appear frequently in the left-handed squark decay and then be detectable at the LHC. In such a case, we showed that the hierarchy of $M_1, M_2$ and $|\mu|$ can be determined. In the light slepton mass scenario with non-vanishing lepton-flavor violation (LFV) in the right-handed sector, NUHM with small $|\mu|$ corresponds to region of parameter space where strong cancellation among leading contributions to $Br(\mu\to e\gamma)$ can occur. We showed that determination of electroweak-ino hierarchy plays a crucial role in resolving cancellation point of $Br(\mu\to e\gamma)$ and determination of LFV parameters. We also discussed test of the universality of the slepton masses at the LHC and the implications to SUSY flavor models.Comment: 34 pages, 16 figure